Search academic texts

Information × Registration Number 0221U105219, 0118U100357 , R & D reports Title The Research of Groups and other Mathematic Structures with Given Systems of Restrictions. popup.stage_title Head Lyman Fedir Mykolayovych, Доктор фізико-математичних наук Registration Date 14-06-2021 Organization Sumy State Pedagogical University named after A. S. Makarenko popup.description2 1) The finite 2-groups with the cyclic center and the non-Dedekind norm of Abelian non-cyclic subgroups is constructively described; 2) The structural characterization of non-periodic locally solvable groups with locally nilpotent non-Dedekind norm of decomposable subgroups is obtained; 3) The structure of norms of Abelian non-cyclic and decomposable subgroups in the class of non-periodic almost locally solvable groups is constructively described, provided that these norms are non-single and have the single intersection. It is established that under such restrictions the norm of decomposable subgroups is a finite cyclic group of prime order, and the norm of Abelian non-cyclic subgroups is an Abelian torsion free group of rank 1 or a finite extension of such a group; 4) The properties of infinite locally finite groups with the locally nilpotent non-Dedekind norm of decomposable subgroups are established and the structural description of such groups is obtained. It was found that locally nilpotent groups with the above restrictions on the norm of decomposable subgroups are locally finite p-groups, and not locally nilpotent such groups are Frobenius groups with an infinite Chernikov kernel, which are finite cyclic extensions of this norm; 5) The properties of "pure" and "mixed" star convergences to the ordinal convergence according to the subdirectional classes, as well as to the convergence with the regulator are studied; 6) Sufficient solvability conditions have been found for a linear weakly perturbed system of integrodynamic Fredholm-type equations with a degenerate nucleus on a time scale of a certain type under the assumption that the corresponding generating system is unsolvable; the iterative procedure for such a solution is developed and its convergence is proved; 7) The image of the fractional part of the real number by series of special types: system fractions, Cantor, Engel, Lurot, Sylvester, Ostrogradsky-Serpinsky-Pierce series, is studied; recursive alg Product Description popup.authors Drushlyak Maryna H Lyman Fedir M Lukashova Tetiana Dmytrivna Pohrebnyi Valerii D Strakh Oleksandr P Khvorostina Yurii Yurii popup.nrat_date 2021-06-14 Close